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<p>This paper explores the existence and the forms of finite order transcendental entire solutions of several quadratic trinomial second order partial differential–difference equations with constant coefficients. We also investigate the forms of solutions of certain quadratic trinomial partial differential equations. A series of examples have been provided to justify the existence and the forms of transcendental entire solution of such equations. Also, the last section of the paper is for a relevant question for future research.</p>

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Entire solutions of the second-order partial differential–difference trinomial functional equations in \(\mathbb {C}^2\)

  • 期刊论文

  • 发表日期：

    2026年7月17日

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  • Tania Biswas,
  • Sayantan Maity

摘要

This paper explores the existence and the forms of finite order transcendental entire solutions of several quadratic trinomial second order partial differential–difference equations with constant coefficients. We also investigate the forms of solutions of certain quadratic trinomial partial differential equations. A series of examples have been provided to justify the existence and the forms of transcendental entire solution of such equations. Also, the last section of the paper is for a relevant question for future research.